Hans Magnus Enzensberger

The German poet and essayist Hans Magnus Enzensberger was an invited speaker at the 1998 International Congress of Mathematicians in Berlin. His talk, analyzing the exclusion of mathematics from the cultural sphere by the public, is the basis of this short book. The text is the bilingual edition of the original work written in German and its English translation by Tom Artin.

First, the author compares and contrasts the public's attitude towards mathematics with intellectual achievements in other fields, such as music, paintings, or literature, and poses the question: "How does it happen that mathematics has remained as it were a blind spot in our culture — alien territory, in which only the elite, the initiate few have managed to entrench themselves?" He acknowledges the use of specialized professional jargon and other communication problems between mathematicians and non-mathematicians, and discusses the traditional perception of pure mathematics as unprofitable and useless, but then, shows the enormous economic value and the somewhat unexpected effectiveness of mathematics in real world problems.

After listing a few highlights of mathematical achievements from Euclid and Eratosthenes to Godel and Andrew Wiles, the author claims that the public should cheer for these intellectual gems at least as much as it celebrates the World Cup football match, Documenta exhibitions, and international theater festivals.

Enzensberger concludes that mathematics instruction may play the key role in the public's attitude towards mathematics. He claims that it "seems a pedagogical idée fixe that children are incapable of abstract thinking." Teachers are "forced to operate at the end of a bureaucratic tether that describes quite brutal curricula and scholastic goals... Nevertheless, it must be said that there are teachers who resist the obsolete routines they are saddled with, and who manage to introduce their students to the beauties, the riches, and the challenges of mathematics. Their successes speak for themselves".

Finally, the author praises the efforts of people such as Martin Gardner, Keith Devlin, Simon Singh, and others, who "specialize in translating the technical jargon of the field into common language", making mathematics more accessible to everybody.

The public's mathematical illiteracy was addressed by many authors, for example by Paulos, in his book Innumeracy. However, there is no quick-fix to the problem. There is a long list of mathematics education reform and anti-reform movements, most of which are related to Enzensberger's point. The dilemma is that all attempts of emphasis on abstract thinking may fail if the teachers are not capable of teaching in that spirit, and all curricula that cuts back on abstract thinking is doomed to produce only drilled number-crunchers, not creative thinkers and problem solvers, who would be able to understand and admire mathematics.

For me, as a mathematics teacher educator, the message was clear: although changing the traditional worldwide ignorance and fear towards mathematics cannot be done overnight, any good teacher can help a little by making mathematics instruction an intellectually engaging and challenging endeavor.

This essay is thought-provoking and a delight to read. Like Constance Reid's From Zero to Infinity, this is also an "insider view of an expert outsider". It is reassuring to know that there are non-mathematicians, who can see and communicate clearly about mathematical issues, and that they care to do so.

Agnes Tuska (agnest@csufresno.edu) is associate professor of mathematics at California State University, Fresno. Her special interests are teacher education and the history of mathematics.